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A variable plane which remains at q cons...

A variable plane which remains at q constant distance `3p` from the origin cut the coordinate axes at `A ,\ B ,\ Cdot` Show that the locus o the centroid of triangle `A B C` is `x^(-2)+y^(-2)+z^(-2)=p^(-2)dot`

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A variable plane which remains at a constant distance 3p from the origin cuts the coordinate axes at A, B, C. Show that the locus of the centroid of triangle ABC is x^(-2) + y^(-2) + z^(-2) = p^(-2) .

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NAGEEN PRAKASHAN ENGLISH-THREE-DIMENSIONAL GEOMETRY -Exercise 11 E
  1. The equation of the line passing through (1, 2, 3) and parallel to the...

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  2. Find the perpendicular distance from the point (2hati-hatj+4hatk) to t...

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  3. Find the perpendicular distance from the point (2hati+hatj-hatk) to th...

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  4. Find the distance of the point (21,0) from the plane 2x+y+2z+5=0.

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  5. Find the distance of each of the following points from the correspondi...

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  6. If the points (1,1,lamda) and (-3, 0,1) are equidistant from the plan...

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  7. Find the distance between the parallel planes 2x-y+3-4=0\ a n d\ 6x-3y...

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  8. Find the distance between the parallel planes, vec r = dot(2 hat i-3 ...

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  9. Find the equations of the planes parallel to the plane x-2y+2z-3=0 whi...

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  10. Find the length of the foot of the perpendicular from the point (1,1,2...

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  11. Find the coordinates of the foot of the perpendicular from the point ...

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  12. Find the image of the point (1,3,4) in the plane 2x-y+z+3=0.

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  13. Find the image of the point O(0,0,0) in the plane 3x+4y-6z+1=0

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  14. A variable plane which remains at q constant distance 3p from the orig...

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  15. Find the distance of the point (1,-2,3) from the plane x-y+z=5 measure...

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  16. Find the distance of the point (0.-3. -2) from the plane x + 2y - z = ...

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  17. Find the equation of the plane passing through the intersection of the...

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  18. Find the equation of the plane through the intersection of the planes ...

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  19. Find the equation of a line passing through the point (2hati-3hatj-5h...

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  20. Find the vector equation of a plane which is at a distance of 5 units ...

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